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- All Subjects: Control Theory
- All Subjects: Gas-turbine disks
- All Subjects: Optimization
- Creators: Mignolet, Marc
Description
As robots are increasingly migrating out of factories and research laboratories and into our everyday lives, they should move and act in environments designed for humans. For this reason, the need of anthropomorphic movements is of utmost importance. The objective of this thesis is to solve the inverse kinematics problem of redundant robot arms that results to anthropomorphic configurations. The swivel angle of the elbow was used as a human arm motion parameter for the robot arm to mimic. The swivel angle is defined as the rotation angle of the plane defined by the upper and lower arm around a virtual axis that connects the shoulder and wrist joints. Using kinematic data recorded from human subjects during every-day life tasks, the linear sensorimotor transformation model was validated and used to estimate the swivel angle, given the desired end-effector position. Defining the desired swivel angle simplifies the kinematic redundancy of the robot arm. The proposed method was tested with an anthropomorphic redundant robot arm and the computed motion profiles were compared to the ones of the human subjects. This thesis shows that the method computes anthropomorphic configurations for the robot arm, even if the robot arm has different link lengths than the human arm and starts its motion at random configurations.
ContributorsWang, Yuting (Author) / Artemiadis, Panagiotis (Thesis advisor) / Mignolet, Marc (Committee member) / Santos, Veronica J (Committee member) / Arizona State University (Publisher)
Created2013
Description
A major concern in the operation of present-day gas turbine engines is the ingestion of hot mainstream gas into rotor-stator disk cavities of the high-pressure turbine stages. Although the engines require high gas temperature at turbine entry for good performance efficiency, the ingested gas shortens the lives of the cavity internals, particularly that of the rotor disks. Steps such as installing seals at the disk rims and injecting purge (secondary) air bled from the compressor discharge into the cavities are implemented to reduce the gas ingestion. Although there are advantages to the above-mentioned steps, the performance of a gas turbine engine is diminished by the purge air bleed-off. This then requires that the cavity sealing function be achieved with as low a purge air supply rate as possible. This, in turn, renders imperative an in-depth understanding of the pressure and velocity fields in the main gas path and within the disk cavities. In this work, experiments were carried out in a model 1.5-stage (stator-rotor-stator) axial air turbine to study the ingestion of main air into the aft, rotor-stator, disk cavity. The cavity featured rotor and stator rim seals with radial clearance and axial overlap and an inner labyrinth seal. First, time-average static pressure distribution was measured in the main gas path upstream and downstream of the rotor as well as in the cavity to ensure that a nominally steady run condition had been achieved. Main gas ingestion was determined by measuring the concentration distribution of tracer gas (CO2) in the cavity. To map the cavity fluid velocity field, particle image velocimetry was employed. Results are reported for two main air flow rates, two rotor speeds, and four purge air flow rates.
ContributorsJunnarkar, Nihal (Author) / Roy, Ramendra P (Thesis advisor) / Mignolet, Marc (Committee member) / Lee, Taewoo (Committee member) / Arizona State University (Publisher)
Created2010
Description
Ingestion of high temperature mainstream gas into the rotor-stator cavities of a gas turbine is one of the major problems faced by the turbine designers. The ingested gas heats up rotor disks and induces higher thermal stresses on them, giving rise to durability concern. Ingestion is usually reduced by installing seals on the rotor and stator rims and by purging the disk cavity by secondary air bled from the compressor discharge. The geometry of the rim seals and the secondary air flow rate, together, influence the amount of gas that gets ingested into the cavities. Since the amount of secondary air bled off has a negative effect on the gas turbine thermal efficiency, one goal is to use the least possible amount of secondary air. This requires a good understanding of the flow and ingestion fields within a disk cavity. In the present study, the mainstream gas ingestion phenomenon has been experimentally studied in a model single-stage axial flow gas turbine. The turbine stage featured vanes and blades, and rim seals on both the rotor and stator. Additionally, the disk cavity contained a labyrinth seal radially inboard which effectively divided the cavity into a rim cavity and an inner cavity. Time-average static pressure measurements were obtained at various radial positions within the disk cavity, and in the mainstream gas path at three axial locations at the outer shroud spread circumferentially over two vane pitches. The time-average static pressure in the main gas path exhibited a periodic asymmetry following the vane pitch whose amplitude diminished with increasing distance from the vane trailing edge. The static pressure distribution increased with the secondary air flow rate within the inner cavity but was found to be almost independent of it in the rim cavity. Tracer gas (CO2) concentration measurements were conducted to determine the sealing effectiveness of the rim seals against main gas ingestion. For the rim cavity, the sealing effectiveness increased with the secondary air flow rate. Within the inner cavity however, this trend reversed -this may have been due to the presence of rotating low-pressure flow structures inboard of the labyrinth seal.
ContributorsThiagarajan, Jayanth kumar (Author) / Roy, Ramendra P (Thesis advisor) / Lee, Taewoo (Committee member) / Mignolet, Marc (Committee member) / Arizona State University (Publisher)
Created2013
Description
Modern life is full of challenging optimization problems that we unknowingly attempt to solve. For instance, a common dilemma often encountered is the decision of picking a parking spot while trying to minimize both the distance to the goal destination and time spent searching for parking; one strategy is to drive as close as possible to the goal destination but risk a penalty cost if no parking spaces can be found. Optimization problems of this class all have underlying time-varying processes that can be altered by a decision/input to minimize some cost. Such optimization problems are commonly solved by a class of methods called Dynamic Programming (DP) that breaks down a complex optimization problem into a simpler family of sub-problems. In the 1950s Richard Bellman introduced a class of DP methods that broke down Multi-Stage Optimization Problems (MSOP) into a nested sequence of ``tail problems”. Bellman showed that for any MSOP with a cost function that satisfies a condition called additive separability, the solution to the tail problem of the MSOP initialized at time-stage k>0 can be used to solve the tail problem initialized at time-stage k-1. Therefore, by recursively solving each tail problem of the MSOP, a solution to the original MSOP can be found. This dissertation extends Bellman`s theory to a broader class of MSOPs involving non-additively separable costs by introducing a new state augmentation solution method and generalizing the Bellman Equation. This dissertation also considers the analogous continuous-time counterpart to discrete-time MSOPs, called Optimal Control Problems (OCPs). OCPs can be solved by solving a nonlinear Partial Differential Equation (PDE) called the Hamilton-Jacobi-Bellman (HJB) PDE. Unfortunately, it is rarely possible to obtain an analytical solution to the HJB PDE. This dissertation proposes a method for approximately solving the HJB PDE based on Sum-Of-Squares (SOS) programming. This SOS algorithm can be used to synthesize controllers, hence solving the OCP, and also compute outer bounds of reachable sets of dynamical systems. This methodology is then extended to infinite time horizons, by proposing SOS algorithms that yield Lyapunov functions that can approximate regions of attraction and attractor sets of nonlinear dynamical systems arbitrarily well.
ContributorsJones, Morgan (Author) / Peet, Matthew M (Thesis advisor) / Nedich, Angelia (Committee member) / Kawski, Matthias (Committee member) / Mignolet, Marc (Committee member) / Berman, Spring (Committee member) / Arizona State University (Publisher)
Created2021
Description
Numerous works have addressed the control of multi-robot systems for coverage, mapping, navigation, and task allocation problems. In addition to classical microscopic approaches to multi-robot problems, which model the actions and decisions of individual robots, lately, there has been a focus on macroscopic or Eulerian approaches. In these approaches, the population of robots is represented as a continuum that evolves according to a mean-field model, which is directly designed such that the corresponding robot control policies produce target collective behaviours.
This dissertation presents a control-theoretic analysis of three types of mean-field models proposed in the literature for modelling and control of large-scale multi-agent systems, including robotic swarms. These mean-field models are Kolmogorov forward equations of stochastic processes, and their analysis is motivated by the fact that as the number of agents tends to infinity, the empirical measure associated with the agents converges to the solution of these models. Hence, the problem of transporting a swarm of agents from one distribution to another can be posed as a control problem for the forward equation of the process that determines the time evolution of the swarm density.
First, this thesis considers the case in which the agents' states evolve on a finite state space according to a continuous-time Markov chain (CTMC), and the forward equation is an ordinary differential equation (ODE). Defining the agents' task transition rates as the control parameters, the finite-time controllability, asymptotic controllability, and stabilization of the forward equation are investigated. Second, the controllability and stabilization problem for systems of advection-diffusion-reaction partial differential equations (PDEs) is studied in the case where the control parameters include the agents' velocity as well as transition rates. Third, this thesis considers a controllability and optimal control problem for the forward equation in the more general case where the agent dynamics are given by a nonlinear discrete-time control system. Beyond these theoretical results, this thesis also considers numerical optimal transport for control-affine systems. It is shown that finite-volume approximations of the associated PDEs lead to well-posed transport problems on graphs as long as the control system is controllable everywhere.
This dissertation presents a control-theoretic analysis of three types of mean-field models proposed in the literature for modelling and control of large-scale multi-agent systems, including robotic swarms. These mean-field models are Kolmogorov forward equations of stochastic processes, and their analysis is motivated by the fact that as the number of agents tends to infinity, the empirical measure associated with the agents converges to the solution of these models. Hence, the problem of transporting a swarm of agents from one distribution to another can be posed as a control problem for the forward equation of the process that determines the time evolution of the swarm density.
First, this thesis considers the case in which the agents' states evolve on a finite state space according to a continuous-time Markov chain (CTMC), and the forward equation is an ordinary differential equation (ODE). Defining the agents' task transition rates as the control parameters, the finite-time controllability, asymptotic controllability, and stabilization of the forward equation are investigated. Second, the controllability and stabilization problem for systems of advection-diffusion-reaction partial differential equations (PDEs) is studied in the case where the control parameters include the agents' velocity as well as transition rates. Third, this thesis considers a controllability and optimal control problem for the forward equation in the more general case where the agent dynamics are given by a nonlinear discrete-time control system. Beyond these theoretical results, this thesis also considers numerical optimal transport for control-affine systems. It is shown that finite-volume approximations of the associated PDEs lead to well-posed transport problems on graphs as long as the control system is controllable everywhere.
ContributorsElamvazhuthi, Karthik (Author) / Berman, Spring Melody (Thesis advisor) / Kawski, Matthias (Committee member) / Kuiper, Hendrik (Committee member) / Mignolet, Marc (Committee member) / Peet, Matthew (Committee member) / Arizona State University (Publisher)
Created2019
Description
All structures suffer wear and tear because of impact, excessive load, fatigue, corrosion, etc. in addition to inherent defects during their manufacturing processes and their exposure to various environmental effects. These structural degradations are often imperceptible, but they can severely affect the structural performance of a component, thereby severely decreasing its service life. Although previous studies of Structural Health Monitoring (SHM) have revealed extensive prior knowledge on the parts of SHM processes, such as the operational evaluation, data processing, and feature extraction, few studies have been conducted from a systematical perspective, the statistical model development.
The first part of this dissertation, the characteristics of inverse scattering problems, such as ill-posedness and nonlinearity, reviews ultrasonic guided wave-based structural health monitoring problems. The distinctive features and the selection of the domain analysis are investigated by analytically searching the conditions of the uniqueness solutions for ill-posedness and are validated experimentally.
Based on the distinctive features, a novel wave packet tracing (WPT) method for damage localization and size quantification is presented. This method involves creating time-space representations of the guided Lamb waves (GLWs), collected at a series of locations, with a spatially dense distribution along paths at pre-selected angles with respect to the direction, normal to the direction of wave propagation. The fringe patterns due to wave dispersion, which depends on the phase velocity, are selected as the primary features that carry information, regarding the wave propagation and scattering.
The following part of this dissertation presents a novel damage-localization framework, using a fully automated process. In order to construct the statistical model for autonomous damage localization deep-learning techniques, such as restricted Boltzmann machine and deep belief network, are trained and utilized to interpret nonlinear far-field wave patterns.
Next, a novel bridge scour estimation approach that comprises advantages of both empirical and data-driven models is developed. Two field datasets from the literature are used, and a Support Vector Machine (SVM), a machine-learning algorithm, is used to fuse the field data samples and classify the data with physical phenomena. The Fast Non-dominated Sorting Genetic Algorithm (NSGA-II) is evaluated on the model performance objective functions to search for Pareto optimal fronts.
The first part of this dissertation, the characteristics of inverse scattering problems, such as ill-posedness and nonlinearity, reviews ultrasonic guided wave-based structural health monitoring problems. The distinctive features and the selection of the domain analysis are investigated by analytically searching the conditions of the uniqueness solutions for ill-posedness and are validated experimentally.
Based on the distinctive features, a novel wave packet tracing (WPT) method for damage localization and size quantification is presented. This method involves creating time-space representations of the guided Lamb waves (GLWs), collected at a series of locations, with a spatially dense distribution along paths at pre-selected angles with respect to the direction, normal to the direction of wave propagation. The fringe patterns due to wave dispersion, which depends on the phase velocity, are selected as the primary features that carry information, regarding the wave propagation and scattering.
The following part of this dissertation presents a novel damage-localization framework, using a fully automated process. In order to construct the statistical model for autonomous damage localization deep-learning techniques, such as restricted Boltzmann machine and deep belief network, are trained and utilized to interpret nonlinear far-field wave patterns.
Next, a novel bridge scour estimation approach that comprises advantages of both empirical and data-driven models is developed. Two field datasets from the literature are used, and a Support Vector Machine (SVM), a machine-learning algorithm, is used to fuse the field data samples and classify the data with physical phenomena. The Fast Non-dominated Sorting Genetic Algorithm (NSGA-II) is evaluated on the model performance objective functions to search for Pareto optimal fronts.
ContributorsKim, Inho (Author) / Chattopadhyay, Aditi (Thesis advisor) / Jiang, Hanqing (Committee member) / Liu, Yongming (Committee member) / Mignolet, Marc (Committee member) / Rajadas, John (Committee member) / Arizona State University (Publisher)
Created2016
Description
In order to achieve higher gas turbine efficiency, the main gas temperature at turbine inlet has been steadily increased from approximately 900°C to about 1500°C over the last few decades. This temperature is higher than the maximum acceptable temperature for turbine internals. The hot main gas may get ingested into the space between rotor and stator, the rotor-stator disk cavity in a stage because of the pressure differential between main gas annulus and the disk cavity. To reduce this ingestion, the disk cavity is equipped with a rim seal; additionally, secondary (purge) air is supplied to the cavity. Since the purge air is typically bled off the compressor discharge, this reducing the overall gas turbine efficiency, much research has been carried out to estimate the minimum purge flow necessary (cw,min) for complete sealing of disk cavities.
In this work, experiments have been performed in a subscale single-stage axial turbine featuring vanes, blades and an axially-overlapping radial-clearance seal at the disk cavity rim. The turbine stage is also equipped with a labyrinth seal radially inboard. The stage geometry and the experimental conditions were such that the ingestion into the disk cavity was driven by the pressure asymmetry in the main gas annulus. In the experiments, time-averaged static pressure was measured at several locations in the main annulus and in the disk cavity; the pressure differential between a location on the vane platform close to lip (this being the rim seal part on the stator) and a location in the 'seal region' in the cavity is considered to be the driving potential for both ingestion and egress. Time-averaged volumetric concentration of the tracer gas (CO2) in the purge air supplied was measured at multiple radial locations on the stator surface. The pressure and ingestion data were then used to calculate the ingestion and egress discharge coefficients for a range of purge flow rates, employing a simple orifice model of the rim seal. For the experiments performed, the egress discharge coefficient increased and the ingestion discharge coefficient decreased with the purge air flow rate. A method for estimation of cw,min is also proposed.
In this work, experiments have been performed in a subscale single-stage axial turbine featuring vanes, blades and an axially-overlapping radial-clearance seal at the disk cavity rim. The turbine stage is also equipped with a labyrinth seal radially inboard. The stage geometry and the experimental conditions were such that the ingestion into the disk cavity was driven by the pressure asymmetry in the main gas annulus. In the experiments, time-averaged static pressure was measured at several locations in the main annulus and in the disk cavity; the pressure differential between a location on the vane platform close to lip (this being the rim seal part on the stator) and a location in the 'seal region' in the cavity is considered to be the driving potential for both ingestion and egress. Time-averaged volumetric concentration of the tracer gas (CO2) in the purge air supplied was measured at multiple radial locations on the stator surface. The pressure and ingestion data were then used to calculate the ingestion and egress discharge coefficients for a range of purge flow rates, employing a simple orifice model of the rim seal. For the experiments performed, the egress discharge coefficient increased and the ingestion discharge coefficient decreased with the purge air flow rate. A method for estimation of cw,min is also proposed.
ContributorsSingh, Prashant (Author) / Roy, Ramendra P (Thesis advisor) / Mignolet, Marc (Thesis advisor) / Lee, Taewoo (Committee member) / Arizona State University (Publisher)
Created2014
Description
The focus of this dissertation is first on understanding the difficulties involved in constructing reduced order models of structures that exhibit a strong nonlinearity/strongly nonlinear events such as snap-through, buckling (local or global), mode switching, symmetry breaking. Next, based on this understanding, it is desired to modify/extend the current Nonlinear Reduced Order Modeling (NLROM) methodology, basis selection and/or identification methodology, to obtain reliable reduced order models of these structures. Focusing on these goals, the work carried out addressed more specifically the following issues:
i) optimization of the basis to capture at best the response in the smallest number of modes,
ii) improved identification of the reduced order model stiffness coefficients,
iii) detection of strongly nonlinear events using NLROM.
For the first issue, an approach was proposed to rotate a limited number of linear modes to become more dominant in the response of the structure. This step was achieved through a proper orthogonal decomposition of the projection on these linear modes of a series of representative nonlinear displacements. This rotation does not expand the modal space but renders that part of the basis more efficient, the identification of stiffness coefficients more reliable, and the selection of dual modes more compact. In fact, a separate approach was also proposed for an independent optimization of the duals. Regarding the second issue, two tuning approaches of the stiffness coefficients were proposed to improve the identification of a limited set of critical coefficients based on independent response data of the structure. Both approaches led to a significant improvement of the static prediction for the clamped-clamped curved beam model. Extensive validations of the NLROMs based on the above novel approaches was carried out by comparisons with full finite element response data. The third issue, the detection of nonlinear events, was finally addressed by building connections between the eigenvalues of the finite element software (Nastran here) and NLROM tangent stiffness matrices and the occurrence of the ‘events’ which is further extended to the assessment of the accuracy with which the NLROM captures the full finite element behavior after the event has occurred.
i) optimization of the basis to capture at best the response in the smallest number of modes,
ii) improved identification of the reduced order model stiffness coefficients,
iii) detection of strongly nonlinear events using NLROM.
For the first issue, an approach was proposed to rotate a limited number of linear modes to become more dominant in the response of the structure. This step was achieved through a proper orthogonal decomposition of the projection on these linear modes of a series of representative nonlinear displacements. This rotation does not expand the modal space but renders that part of the basis more efficient, the identification of stiffness coefficients more reliable, and the selection of dual modes more compact. In fact, a separate approach was also proposed for an independent optimization of the duals. Regarding the second issue, two tuning approaches of the stiffness coefficients were proposed to improve the identification of a limited set of critical coefficients based on independent response data of the structure. Both approaches led to a significant improvement of the static prediction for the clamped-clamped curved beam model. Extensive validations of the NLROMs based on the above novel approaches was carried out by comparisons with full finite element response data. The third issue, the detection of nonlinear events, was finally addressed by building connections between the eigenvalues of the finite element software (Nastran here) and NLROM tangent stiffness matrices and the occurrence of the ‘events’ which is further extended to the assessment of the accuracy with which the NLROM captures the full finite element behavior after the event has occurred.
ContributorsLin, Jinshan (Author) / Mignolet, Marc (Thesis advisor) / Jiang, Hanqing (Committee member) / Oswald, Jay (Committee member) / Spottswood, Stephen (Committee member) / Rajan, Subramaniam D. (Committee member) / Arizona State University (Publisher)
Created2020
Description
The problem of modeling and controlling the distribution of a multi-agent system has recently evolved into an interdisciplinary effort. When the agent population is very large, i.e., at least on the order of hundreds of agents, it is important that techniques for analyzing and controlling the system scale well with the number of agents. One scalable approach to characterizing the behavior of a multi-agent system is possible when the agents' states evolve over time according to a Markov process. In this case, the density of agents over space and time is governed by a set of difference or differential equations known as a {\it mean-field model}, whose parameters determine the stochastic control policies of the individual agents. These models often have the advantage of being easier to analyze than the individual agent dynamics. Mean-field models have been used to describe the behavior of chemical reaction networks, biological collectives such as social insect colonies, and more recently, swarms of robots that, like natural swarms, consist of hundreds or thousands of agents that are individually limited in capability but can coordinate to achieve a particular collective goal.
This dissertation presents a control-theoretic analysis of mean-field models for which the agent dynamics are governed by either a continuous-time Markov chain on an arbitrary state space, or a discrete-time Markov chain on a continuous state space. Three main problems are investigated. First, the problem of stabilization is addressed, that is, the design of transition probabilities/rates of the Markov process (the agent control parameters) that make a target distribution, satisfying certain conditions, invariant. Such a control approach could be used to achieve desired multi-agent distributions for spatial coverage and task allocation. However, the convergence of the multi-agent distribution to the designed equilibrium does not imply the convergence of the individual agents to fixed states. To prevent the agents from continuing to transition between states once the target distribution is reached, and thus potentially waste energy, the second problem addressed within this dissertation is the construction of feedback control laws that prevent agents from transitioning once the equilibrium distribution is reached. The third problem addressed is the computation of optimized transition probabilities/rates that maximize the speed at which the system converges to the target distribution.
This dissertation presents a control-theoretic analysis of mean-field models for which the agent dynamics are governed by either a continuous-time Markov chain on an arbitrary state space, or a discrete-time Markov chain on a continuous state space. Three main problems are investigated. First, the problem of stabilization is addressed, that is, the design of transition probabilities/rates of the Markov process (the agent control parameters) that make a target distribution, satisfying certain conditions, invariant. Such a control approach could be used to achieve desired multi-agent distributions for spatial coverage and task allocation. However, the convergence of the multi-agent distribution to the designed equilibrium does not imply the convergence of the individual agents to fixed states. To prevent the agents from continuing to transition between states once the target distribution is reached, and thus potentially waste energy, the second problem addressed within this dissertation is the construction of feedback control laws that prevent agents from transitioning once the equilibrium distribution is reached. The third problem addressed is the computation of optimized transition probabilities/rates that maximize the speed at which the system converges to the target distribution.
ContributorsBiswal, Shiba (Author) / Berman, Spring (Thesis advisor) / Fainekos, Georgios (Committee member) / Lanchier, Nicolas (Committee member) / Mignolet, Marc (Committee member) / Peet, Matthew (Committee member) / Arizona State University (Publisher)
Created2020